Makes no difference. Per capita is by the head. Density has nothing to do with it. If the people in South Dakota owned 50 guns each< per person<per capita, then South Dakota would own more guns, per capita than Wyoming.
Here is an example of a study on how healthcare is covered according to density. In order to have a constant to compare counties per density, they used a per capita expenditure as a gauge. That is, what one head, one person, would spend on healthcare:
We execute a cross-sectional analysis of 178 country-level observations. This is represented by equation (
1), in which the subscript
c denotes a country-specific variable. To hold the health system’s resources constant, we include per capita health expenditure...
Regardless of where the per capita (single person) received their health care, this is what one person would be expected to spend on healthcare.
They use per capita as a unit of population. It is equal to each individual of any other state.